P!=NP is a big deal in computational complexity as 1) It would solve one of the most important problems in computer science and mathematics 2) Understanding of

P!=NP is a big deal in computational complexity as 1) It would solve one of the most important problems in computer science and mathematics 2) Understanding of the proof and the methods it uses could very likely lead to solving other problems in computational complexity. 3) Furthermore, the proof would shed light on why certain problems are hard. Such an understanding could lead to better heuristics to solve those problems.